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PlatformYouTube361X3Bilibili2

DisciplineMathematical modeling179Calculus69Algebra50Probability & statistics44Discrete mathematics15Applied mathematics7General mathematics1Geometry1

DifficultyIntroductory242Intermediate76Foundational44Advanced4

StyleWhiteboard171Visual explanation107Lecture86Problem solving2

Length5–15 min213Under 5 min12515–45 min28

TopicMatrices24Derivatives15Probability13Vectors12Integrals12Expectation8Distributions8Greatest common divisor8Time series forecasting8Eigenvalues7Linear transformations7Function limit7Exponential smoothing forecasting7Chain rule6Random variables6Normal distribution6Euclidean algorithm6Graph theory6Determinants5Bayes’ theorem5Basis5Means5Permutations5Function graph5Definite integral5Independence5Game theory modeling5Calculus4Conditional probability4Binomial distribution4Taylor series4Grey prediction model4Regression modeling4ARIMA modeling4Normalization and standardization in modeling4Entropy weight method4Linear programming4Transportation problem4Cluster analysis modeling4Hypothesis testing3Function approximation3Mean value theorem3Partial derivative3Power series3Infinite series3Multivariable function3Fuzzy comprehensive evaluation3Interpolation methods for modeling3Agent-based modeling3System dynamics modeling3Error propagation in models3Dimensional analysis3Principal component analysis3Network flow modeling3Monte Carlo simulation3Markov chain modeling3Cellular automaton model3Minimum spanning tree model3Model validation techniques3Least squares fitting3Inventory model3Assignment problem3Fourier transform2Linear span2Riemann sums2Gradient2Arc length2Lagrange multipliers2Series convergence2Partial sums2Total differential2Jacobian determinant2Variance2Outlier handling in modeling2SIR epidemic model2Logistic growth model2Similarity and scaling in modeling2Model assumptions and simplification2Traveling salesman modeling2Shortest path models2Branch and bound2Structure of a modeling report2Population growth model2Fourier series2Exponential growth2Markov chains2Partial differential equations2Group representations2Sequence convergence2Pointwise convergence2Three-dimensional space1Fractions1Tangent line1Area under curve1Incidence matrix1Network conservation1Line integral of a vector field1Sequence limit definition (ε–N)1Divergence1Function limit definition (ε–δ)1Comparison test1Error estimate1Alternating series1Zeno’s paradox1Limit nonexistence1Secant line1Local linearization1Tangent plane1Normal vector1Directional derivative1Multivariable limit1Iterated integral1Volume under surface1Moment of inertia1Rectangle partition1Curve fitting in modeling1Discriminant analysis1Factor analysis1Optimization modeling1Duality in linear programming1Differential equation modeling1Common mistakes in mathematical modeling1Integer programming1Multi-objective optimization1Dynamic programming for modeling1Queueing model1Analytic hierarchy process1Poisson distribution1Uniform distribution1Zero-knowledge proofs1Simplex method1Yoneda lemma1Topological spaces1Autocorrelation1Trigonometric identities1Logistic growth1Universal properties1Value at Risk1Proof by contradiction1Direct proof1Analysis of variance1Experimental design1Angles1Rigid motions1Well-posedness1Complete reducibility1Difference equation model1Sequence limit1Nash equilibrium1Brownian motion1Counterexamples1Linear regression1Verification and validation1Finite element method1Connectedness1Uniform convergence1Turing patterns1Weak convergence1Quadratic residues1Modular arithmetic1Number theory1Analytic continuation1Compound interest1Singular values1Absolute value1Almost everywhere1Lebesgue measure1Triangle congruence1Bipartite matching1Chain complexes1Trees1Bisection method1Fields1TOPSIS evaluation model1Compact operators1Bounded linear operators1Unit circle1Unique factorization domains1Binary operations1Differential forms1Isolated singularities1Laurent series1Schur's lemma1Area and volume1Matrix norms1Monotone convergence theorem1Mathematical induction1Transition matrices1Chi-squared distribution1

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Mathematical modeling·English

Number Theory | Quadratic Residues: Definition and Examples

Michael Penn

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